Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C2×C4×#3802 |
| Fitting | C2×C32×C42 ⋊ C22 |
| Sylow | C32 ⋊ C22×C4×D4 |
5305 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11902357, #72219770, #72219796, … |
| maximal normal subgroup of | C2×#11902357, #72219770, #72219796, … |
| maximal quotient of | #72214070, #72222726, C2×#11861057 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 133909);